Dissecting the vascular-cognitive nexus: energetic vs. conventional hemodynamic parameters

Blood pressure or flow measurements have been associated with vascular health and cognitive function. We proposed that energetic hemodynamic parameters may provide a more nuanced understanding and stronger correlation with cognitive function, in comparisons with conventional aortic and carotid pressure and flow parameters. The study comprised 1858 participants, in whom we assessed cognitive function via MoCA method, and measured central aortic and carotid pressure and flow waveforms. In addition to various pressure and flow parameters, we calculated energetic hemodynamic parameters through integration of pressure multiplying flow with respect to time. Energetic hemodynamic parameters, particularly aortic and carotid mean and pulsatile energy and pulsatility index (PI), were significantly associated with MoCA score more than any aortic and carotid pressure and flow parameters, after adjusting for age, sex, education, depression score, heart rate, BMI, HDL-cholesterol, and glucose levels. MoCA exhibited a strong positive relationship with carotid mean energy (standardized beta = 0.053, P = 0.0253) and a negative relationship with carotid energy PI (standardized beta = −0.093, P = 0.0002), exceeding the association with all traditional pressure- or flow-based parameters. Aortic pressure reflection coefficient at the aorto-carotid junction was positively correlated with mean carotid energy and negatively correlated with PI. Aortic characteristic impedance positively correlated with carotid energy PI but not mean energy. Our research indicates that energetic hemodynamic parameters, particularly carotid mean energy and carotid energy PI, have a stronger association with MoCA scores than traditional pressure- or flow-based metrics. This correlation with cognitive function is notably influenced by the properties of the aorto-carotid interface.


Background
Cognitive decline and dementia are escalating global health concerns, especially within aging populations [1,2].A robust body of evidence links vascular dementia with hemodynamic abnormalities stemming from various cardiovascular conditions [3].High blood pressure, for example, compromises the cerebral vasculature and predisposes individuals to cognitive impairment, especially when it develops earlier in life [4][5][6][7].
Traditionally, carotid hemodynamics have been a focus of study given their role in cerebral blood supply.Changes in carotid pressure and flow waveforms have been linked to cognitive impairment.As a result, different parameters derived from pressure or flow have been developed to improve the ability to predict patient outcomes [8][9][10][11].We previously demonstrated that lower carotid flow velocity was frequently associated with smaller cerebral white matter and gray matter volume [9], and has been regarded as a strong indicator of brain atrophy and an effective predictor of increased risk of stroke [8,12].Previous research has

Clinical relevance
Energetic hemodynamic parameters, specifically carotid energy PI and carotid mean energy, are crucial indicators for evaluating cognitive function and are more effective than traditional vascular metrics.

Future direction
Prospective studies are required to establish causality and validate findings using cognitive assessment tools with different levels of sensitivity.This may involve including a wider range of cognitive functions in the study population.

Consideration for the Asian population
This study investigates the relationship between carotid hemodynamics and cognitive function in Asian ethnic groups, motivated by the growing risk of dementia in rapidly aging populations in Asian countries.

Novelty and Relevance
What Is New?
• Carotid energy PI is a significant indicator of cognitive health.
• MoCA scores are more closely linked to energetic hemodynamics than conventional flow or pressurebased assessment.

Relevance to Hypertension
• Vascular aging plays a crucial role in the pathophysiology of hypertension.
• This research suggests that energy-based hemodynamic parameters may better predict cognitive decline due to vascular aging in hypertension patients.

Clinical/Pathophysiological Implications
• Assessing the vascular-cognitive nexus may be more effective using carotid energetic hemodynamic parameters than pressure or flow-based frameworks.
• Targeting hemodynamic changes may aid cognitive preservation strategies.
The study suggests a stronger link between vascular and cognitive health, which could inform future treatme Graphical Abstract emphasized parameters like pressure and flow pulsatility indexes (PIs) for their associations with cerebrovascular diseases and cognitive decline [12,13].
The "impedance mismatch" hypothesis has been proposed to illustrate vascular aging-related target organ damage.The hypothesis states that pulsatile energy is not fully transmitted into the distal vasculature because impedance mismatch at the junction of the highly compliant aorta and relatively stiff first-generation branch vessels limits transmission of pulsatile power/energy into the carotid artery [14].Vascular aging of proximal aorta erodes impedance mismatch and promotes transmission of excess pulsatile energy into the carotid arteries [14].An inclusive comprehension of systemic or organ hemodynamics typically necessitates the acquisition of both pressure and flow data.Traditional metrics, which were primarily derived from pressure or flow alone, might not totally comprise the complex interaction between vascular and cognitive functions.We therefore proposed that energetic hemodynamic parameters may provide a more comprehensive and nuanced framework for analyzing this complex relationship and patient's outcome prediction [14].

Study cohorts
The present study cohort comprised two study populations, the Cardiovascular and Disease Risk Factors Two-Township Study (CVDFACTS) and the Longitudinal Aging Study of Taipei (LAST).CVDFACTS is an ongoing longitudinal study of the risk factors and pathogenesis of cardiovascular disease in two Taiwanese cities, Chu-Dung (a Hakka community) and Pu-Tzu (a Fukienese community) [15].Residents who were aged 30 and over and previously participated in one or more of CVDFACTS surveys were recruited from 2017 through 2020.The Longitudinal Aging Study of Taipei (LAST) is an ongoing community-based study that was initiated by Aging and Health Research Center of the National Yang Ming Chiao Tung University from May 2016 to December 2019, a total of 1532 community volunteers were invited to participate the first wave of the study.The criteria for including and excluding participants in two cohorts are as follows: the inclusion criteria are individuals who agreed to take part in the cohort studies and follow-up.The exclusion criteria consist of individuals with poor activities of daily living, long-term bedridden individuals, those unable to complete the questionnaire due to communication challenges, individuals with a life expectancy of less than 6 months, arrhythmia, heart failure, severe valvular heart disease, individuals diagnosed with dementia, and other neurodegenerative diseases such as Parkinson's disease.
For the cardiovascular hemodynamic assessments, these two study cohorts have adopted the same study protocol, which has been approved by the Institutional Review Board of National Yang Ming Chiao Tung University.Each participant was well-informed, and a written consent was obtained before the study.
All subjects were scheduled for two visits within 3 months for the study.Information of personal characteristics, prior medical history, anthropometric measurements, cognitive function, and fasting blood tests were collected during the first visit.Medical history, particularly stroke and heart diseases, was acquired by structured questionnaires.An example was as follows: "Did you have heart disease diagnosed by a physician at a clinic or hospital?"Cardiovascular hemodynamic measurements were conducted during the second visit.We used structured questionnaires, the Center for Epidemiologic Studies Depression Scale and Taiwanese Depression Scale in LAST cohort and CVDFACTS cohort, respectively, to measure depression.The depression scales of these two cohorts were then normalized for further analysis.

Cognitive function
The global cognitive function was evaluated using the Montreal Cognitive Assessment (MoCA) protocol with the Chinese version specifically used in Taiwan [16], through face-to-face interview by dedicated and qualified nurses adherent to the standardized study guide.The MoCA was constituted by 20 items clustered into 7 subgroups, each dedicated to one aspect of cognitive function, namely executive function/visuospatial ability (5 points), attention (6 points), animal naming (3 points), language (3 points), abstraction (2 points), short-term memory (5 points), and orientation (6 points) with a total score of 30 points [17].

Echocardiography
Participants all received transthoracic echocardiography performed by an experienced sonographer.All images were acquired using a commercially available machine (HD11 XE Ultrasound system, Koninklijke Philips N.V.) and digitized using the TomTec Image-Arena™ Software 4.0 (TomTec Imaging Systems GmbH, Munich, Germany) by the same sonographer.Left ventricular (LV) volume was acquired by tracing the endocardial border of the left ventricle at both the end-diastole and end-systole, then summing up a stack of elliptical disks in apical 4-chamber view.The determination of LV ejection fraction involved calculating the discrepancy between the volume of the left ventricle at the end of diastole and the volume at the end of systole.Doppler-derived stroke volume was the product of the cross-sectional area and the velocity, calculated via Doppler signal acquired at the LV outflow tract during systole [18].Doppler-derived cardiac output was calculated as the product of stroke volume and heart rate.Cardiac index (CI) was calculated as cardiac output divided by the body surface area [18].

Arterial stiffness
Arterial waveforms at the right common carotid artery (CCA) and the right femoral artery were recorded in sequence, by means of applanation tonometry using a pencil-type tonometer, a high-fidelity strain-gauge transducer at the flat tip of 7-mm-diameter (SPC-350, Millar Instruments Inc, Texas) [19].Body surface measurements from carotid to femoral pulse recording sites were obtained by tape measure.Carotidfemoral pulse wave velocity (cf-PWV) was calculated as the distance between the two measurement sites, divided by the foot-to-foot wave transit time.Transit time was calibrated by the simultaneously recorded ECG, and aligned via a customdesigned software on a commercial software package (Matlab, version 4.2, The MathWorks, Inc.) [19].

Data acquisition and analysis
Each recording lasted for 25 s (5-6 respiratory cycles) to ensure steady and high-quality pulse waveforms.Each waveform admitted for subsequent hemodynamic analysis was an average of 10 consecutive steady waveforms.The aortic pressure was determined by the tonometry waveform measured at the right CCA, calibrated by simultaneously measured mean and diastolic pressure of the brachial cuff pressure.Measurements of central aortic and carotid blood flows were performed by the same healthcare professional to maintain quality consistency.Central aortic blood flow, was determined as the Doppler flow velocity, measured using a pulsed-wave Doppler echocardiography at the LV outflow tract in an apical five-chamber view, multiplied by the cross-sectional area at the LV outflow tract on a parasternal long-axis views.The flow velocity (waveform) was measured from the envelope as a spatially averaged mean value for the subsequent calculation of the flow PI and energy parameters.The left and right common carotid flows were determined by the Doppler velocity waveform, recorded using a linear array probe with 3.1-10.0MHz imaging frequency in the longitudinal view.The sample volume was placed at the center of the CCA around 1 cm proximal to the carotid bulb.Flow velocities were multiplied by the respective carotid lumen cross-sectional area to get volumetric flow rate.The carotid arterial diameter was measured from the intima-lumen interface of the near wall to the lumen-intima interface of the far wall.All Doppler measurements were obtained with an insonation angle maintained ≤60°.The carotid flow waveform images were digitized and transformed into a signal-averaged flow spectrum in the MATLAB program.Each velocity waveform admitted for subsequent analysis was an average of 10 consecutive waveforms.Since the pressure at ascending aorta is largely comparable to the pressure at carotid artery, the measured carotid arterial pressure waveform was adopted as the aortic pressure waveform to be paired with the corresponding aortic flow for hemodynamic analysis.Given that the passage of a wave causes simultaneous changes in both pressure and flow waveform, arterial pressure waveform was shifted in time so that the onset of systolic pressure matches that of the blood flow waveform.For carotid hemodynamic analysis, the carotid blood flow admitted for hemodynamic analysis was the sum of both the left and right carotid blood flows.

Hemodynamic analysis
The mean and pulsatile hydraulic energy In this study, we calculated the hydraulic mean, pulsatile energy, and total energy for one cardiac cycle, consistent with those power-based parameters adopted by Haidar et al. [20].To calculate the hydraulic mean and pulsatile energy for one cardiac cycle, we first separated the measured pressure P (t) and blood flow Q (t) waveforms into their respective mean and pulsatile components: Total and pulsatile hydraulic energy, E, of one cardiac cycle, T, was calculated as the product of pressure P (t) and flow Q (t) or pulsatile pressure P p (t) and flow Q p (t), respectively, integrated with respect to time t over T. Calculations were repeated for both aorta and carotid artery.In addition, we computed an effective accumulating "mean" energy, as P Â Q Â t (Fig. 1 and Supplementary Table 1).Figure 1 provides a detailed depiction of the pressure, flow, and energy waveforms at the aorta and carotid arteries, accompanied by the relevant equations [20].

Aortic and carotid wave pressure, flow and energy reflection, and reflection coefficients
In this study, the aorto-carotid junction was simplified by a bifurcation [20], by which the central aorta was presumed branching into two asymmetric daughter vessels, a larger downstream thoracic aorta, and a smaller carotid artery.The carotid blood flow was calculated as a linear sum of both the left and right carotid flow since both sides of blood flow influenced cognitive function [20].
The aortic forward-going wave (defined as the direction of the mean blood flow) pressure reflection coefficient at the aorto-carotid junction, Γ Ao , was calculated as where A Ao , A carotid , A thoracic were the admittance of the proximal aorta, the carotid artery and the downstream thoracic aorta, respectively.The admittance is the reciprocal of impedance.At aorta and carotid artery, admittance was calculated as the averaged ratio of magnitudes of flow to magnitudes of pressure from the 2nd harmonic through the 10 th harmonic in frequency domain.At thoracic aorta, admittance was calculated as A Ao multiplied by the ratio of thoracic mean flow, which was the difference between the aortic mean flow and the carotid mean flow, divided by aortic mean flow, following the assumption that the local pulse wave velocity and mean flow velocity were presumed uniform across aorta just proximal of the bifurcation junction and distal thoracic artery [15].By definition, the aggregate forward-going flow wave reflection coefficient at the aorto-carotid junction was Γ Ao .

Statistical methods
Continuous and categorical characteristics of the sample were described by mean (± standard deviation) and percentage, respectively.For the baseline model, the partial correlation coefficients between MoCA score and aortacarotid arterial hemodynamics were computed by adjusting for age, sex, education, depression score, and heart rate.For the fully adjusted model, we further adjusted for other potential confounders including body mass index, and LDL-cholesterol, and fasting glucose, for the associations between MoCA score and aorta-carotid arterial hemodynamics in addition to the baseline model.Three steps were required to conclude the energy calculation.The first step was to calculate the total, mean, and pulsatile power as a function of time (the 2nd right column).The total power (black curve) was calculated as the product of concurrent aortic pressure (black curve, the 1st left column) and aortic flow (black curve, the 2nd left column).Similarly, the mean power (red dash-dot curve) and pulsatile power (blue solid curve) were calculated as the product of concurrent mean pressure and mean flow (red dash-dot curve) and concurrent pulsatile pressure and pulsatile flow, respectively.The second step was to calculate the total, mean, and pulsatile energy, by integrating the total, mean, and pulsatile power with respect to time (the 1st right column).
The third step, the potential energy as a function of time (green dashed curve) was calculated as the instantaneous difference between the total energy (black curve) and the sum of the mean (red dash-dot curve) and pulsatile energy (blue solid curve; the 1st right column).Note that the total energy was not equal to mean energy plus pulsatile energy until the end of a cycle The Pearson correlation matrix was conducted for the interrelations of carotid energy PI, carotid flow PI, aortic energy PI, aortic pressure PI, and aortic flow PI.Correlations between carotid total, mean and pulsatile energy with aortic total, mean and pulsatile energy, aortic forward wave pulsatile energy transmitted into carotid artery, and Γ Ao were examined by using the Pearson correlation.The correlations between carotid mean and pulsatile energy and carotid energy PI were identified by general linear models.
We employed causal mediation models to examine the relations between Z ao and cognitive function.Additionally, we investigated whether these associations were mediated by the carotid energy PI and carotid mean energy, or by the carotid flow PI and carotid mean flow.Furthermore, we explored the associations between aortic pressure wave reflection coefficient Γ Ao and the cognitive function.
We also examined whether these associations were mediated by the carotid energy PI and carotid mean energy, or by the carotid flow PI and carotid mean flow.The statistic significant p value was dependent on the multiple comparison testing.
The Path analysis, involving causal mediation models, was conducted using the CALIS procedure in SAS 9.4.The performance of all models was assessed using the goodness of fit index (GFI).The significance level was established at a value of 0.05.

Results
Clinical characteristics and hemodynamic parameters of all 1858 participants are summarized in Table 1.Females had a higher average age, and HDL-cholesterol than males.Males had more hypertension and diabetes than females.Males had more university degrees than females.Men and women had a median Montreal cognitive score of 27.
The carotid mean flow was found to be approximately 30.3% of the aortic mean flow.Additionally, the carotid pulsatile flow was observed to be around 10.2% of the aortic pulsatile flow.Consequently, the carotid flow PI was calculated to be approximately 34.5% of the aortic flow PI.The energy PI of the carotid artery was found to be 37.9% when compared to the aortic counterparts, as indicated in Table 2.A comparative analysis of flow and energy metrics between female and male at ascending aorta and CCA is summarized in Table 2.As expected, male exhibited higher mean and peak flow rate and total energy at both ascending aorta and carotid artery.Still, there were no significant differences between male and female in terms of energy pulsatility at both sites.
The MoCA score were significant associations with variables such as age, education level, blood pressure, fasting glucose levels, and lipid profiles, as indicated in Supplementary Table 2.After adjusting for age, sex, educational attainment, and depression levels, only certain variables, namely peripheral mean pressure, waist circumference, body mass index, high density lipoprotein cholesterol, total cholesterol, and fasting blood sugar, continued to exhibit a significant association with MoCA.The associations between MoCA score and different hemodynamic parameters are displayed in Table 3.The MoCA scores demonstrated inverse relationships with the aortic mean, pulse and systolic pressure, and aortic energy PI, and carotid flow PI.Conversely, a positive correlation was observed with the carotid mean energy.As summarized in Table 3, the hemodynamic parameters of the carotid artery demonstrated a more robust correlation with the MoCA scores as compared to those of the aorta.Furthermore, the investigation revealed that parameters based on energy, specifically the mean and pulsatile energy in the carotid artery, along with the pulsatility index (PI) of energy, exhibited significantly stronger correlations with MoCA scores than any parameters based on pressure or flow, including mean, peak, and pulse pressure or flow in both the aorta and carotid arteries.Further analysis revealed that the carotid energy PI emerged to have the most significant correlation with cognitive function (r = −0.097),after adjusting for various confounding factors, including age, gender, level of education, and various health indicators, as well as analyzing against conventional hemodynamic parameters, namely aortic or carotid systolic, mean and pulse pressure or flow.The second most significantly correlated parameter was the carotid flow PI (r = −0.085),followed by the aortic energy PI (r = −0.080),as depicted in Fig. 2A.
In the comparative analysis presented in Table 4, it was found that, after adjusting for age, sex, and education, along with their respective pulsatility index (PI) indices, both the carotid flow PI (as depicted in Model 1 of Table 4) and the aortic energy PI (as depicted in Model 2 of Table 4) ceased to be significantly associated with cognitive function.We further performed a stratified analysis by age.Due to the limited number of participants above the typical age threshold of 65 for older adults, we adopted the cutoff age to 60 years, which allowed us to classify the subjects into the older cohort and the younger cohort.The results revealed the relationship between hemodynamic parameters and MoCA varies between elderly and young populations.As shown in Fig. S1, significant associations of hemodynamic parameters, particularly energetic hemodynamic parameters, are mainly seen in the older population.
Table 5 summarized the correlations of carotid mean energy, carotid energy PI, and carotid PI with aortic pressure, flow, energetic metrics and cf-PWV, Z ao , and Γ Ao .Notably, carotid mean energy correlates positively with both aortic mean (r = 0.126) and peak flow (r = 0.11), with all p < 0.0001.The carotid energy PI also shows a positive correlation with aortic mean flow (r = 0.104) and a weaker one with peak flow (r = 0.082).Additionally, the carotid PI has robust positive associations, especially with aortic peak flow (r = 0.186).Significant correlations were noted between Z ao and both carotid energy PI and carotid PI.Furthermore, there is an inverse relationship between the reflection coefficient at the aorto-carotid junction, Γ Ao , and carotid energy PI and flow PI, whereas carotid mean energy positively correlates with Γ Ao .
The analysis presented in Fig. 3 clearly demonstrates the impact of carotid energy PI and carotid mean energy on MoCA scores.The impact of Z ao and Γ Ao on MoCA is solely mediated through energy metrics, without any direct influence.On the other hand, the flow-based analysis places emphasis on the contribution of flow pulsatility to the MoCA, ascribing significant direct effects to both Z ao (with borderline significance) and Γ Ao .

Discussion
This study emphasizes the unique importance of energetic parameters in comprehending the connection between vascular health and cognitive function.The initial analysis revealed a clear beneficial relationship between carotid mean energy and cognitive function, while a negative relationship was observed with pulsatile energy.Our research represents a painstaking effort to identify the carotid energy PI as a more effective hemodynamic indicator for cognitive function.Furthermore, after conducting a thorough evaluation of numerous hemodynamic parameters related to the aorta and carotid artery, it has been established that the carotid energy PI emerges as the most prominent indicator for predicting the cognitive performance, surpassing all available conventional pressure-or flow-based metrics.We subsequently conducted an extensive investigation into the carotid energy PI and carotid mean energy, in relation to aortic flow and energy indices, aortic stiffness, aorto-carotid impedance mismatch, and organ perfusion.
The aorto-carotid impedance mismatch has long been regarded playing a critical role in cognitive function.We showed that an increase in proximal aortic stiffness is a contributing factor to the elevated pulsatile energy observed in the carotid arteries, whereas the influence of aortic stiffness, Z ao , and the wave reflection coefficient, Γ Ao , on MoCA predominantly manifests itself through energy metrics, rather than through direct effects.In contrast, a flow-based assessment underscored the fundamental importance of flow pulsatility in the MoCA.Significant direct effects were ascribed to both Z ao and Γ Ao .However, it is conceivable that this assessment may have placed  Dissecting the vascular-cognitive nexus: energetic vs. conventional hemodynamic parameters excessive emphasis on the importance of wave reflection in the pathophysiological connection between vascular health and cognitive impairment.Hence, our research approach, which is based on the concept of energy, focuses on the complex impact of energy pulsations on cognitive function.This approach contributes to a comprehensive understanding of the interconnected relationship between vascular health and cognitive function.
Our research comprehensively elucidates the fundamental mechanisms that govern the transfer of increased circulatory pulsatility from a stiffened aorta to cerebral circulation and demonstrated the connection and significant impact of the "impedance mismatch" phenomenon with cognitive function.The hemodynamic energy in carotid arteries is linked to aortic hemodynamic energy produced by the LV contraction and is inversely related to the reflection coefficient at the aorto-carotid junction, which is influenced by aortic and carotid admittance/compliance.During youth, aortic compliance exceeds carotid compliance, resulting in a high reflection coefficient known as "impedance mismatch".As individuals grow older, there is a noticeable increase in impedance "matching", which can be attributed to a greater increase in aortic impedance as compared to impedance of first-generation branch vessels.This impedance matching leads to heightened transmission of pressure and flow pulsatility into the cerebral circulation, ultimately strengthening the connection between the cardiac and cerebral structures and their respective functions [14].Figure S1 illustrates that variations in connections could be attributed to the scarcity of individuals with cognitive decline in the younger population and the concept of impedance mismatch.Strong correlations between hemodynamic parameters, especially energetic ones, are predominantly observed in the elderly.These observations align with the gradual stiffening of the proximal aorta, as depicted in Figs.S2, S3, and S4.Furthermore, our analysis comprehensively investigates the substantial impacts of the carotid energy PI and carotid mean energy on MoCA scores.
This observation implies that the flow-based approach may potentially exaggerate the extent to which wave reflection contributes to the preservation of pulsatility, while simultaneously overlooking its influence in amplifying mean energy.By employing the energy-based methodology, it is possible to distinguish the heightened influence of energy pulsatility compared to mean energy on the MoCA, with Z ao playing a noteworthy role.Nevertheless, the contributions of protective effects resulting from reflections at the interface between the aorta and carotid artery are somewhat limited.
Our finding was consistent with that of the AGES-Reykjavik Study, where the pulsatile power (pulsatile energy normalized by the period of a cardiac cycle) was negatively associated with cognitive function [20].In the present study, we further demonstrated the counteractive effect of the positive association between carotid mean energy and cognitive function was comparable to the negative association between carotid pulsatile energy and MOCA score (standardized Beta: 0.117 vs. -0.109).

Study strengths and limitations
There are several strengths in this study.First, we showed that the carotid mean energy and the pulsatile energy were positively and negatively associated with cognitive function, respectively.Considering that this is the first study to identify the carotid energy PI as the best hemodynamic indicator for cognitive function, our study findings should be reproduced by other studies.Second, through extensive evaluation of exhaustive aorto-carotid hemodynamic parameters, we concluded that the carotid energy PI is the single most effective hemodynamic parameter for predicting cognitive function, much more effective than any other available hemodynamic parameters proposed previously.Third, our study populations had a broad age-range between 31 and 96 years old, not limited to aging population.Two weakness were also noted in this study.Since our study was a cross-sectional design, the causality inference may be inappropriate.Further prospective studies need for elucidate this relationship.Second, the method to evaluate cognitive function in this study was MoCA, which was more sensitive than MMSE [21].Future research endeavors could entail external validation studies that employ cognitive function assessment tools possessing varied levels of sensitivity.Additionally, these studies might consider incorporating a more expansive distribution of cognitive function within the study population, coupled with prospective follow-up, to enhance the comprehensiveness and reliability of the findings.
The simplified aorto-carotid junction as an asymmetric bifurcation did not include blood flows to branches of the left and right subclavian artery.Still, we consider that by including them would not fundamentally alter the results of our analysis, since there is no evidence to show significant changes in neither subclavian blood flow nor arterial properties during the progression of cognitive decline.

Perspective of Asia
This study investigated the relationships between carotid hemodynamics and cognitive function in Asian ethnic groups.These areas are confronted with a substantial societal dilemma as a result of the escalating threat of dementia brought about by their swiftly aging populations.According to a study [22], the Asian group shows a greater rate of cognitive decline in comparison to the white group.Further investigation is necessary to determine if the difference can be attributed to cardiovascular and neurological complications.Our study commences an inquiry into a noteworthy mechanism and its potential future clinical uses.

Conclusion
Our study reveals that energetic hemodynamic parameters, especially carotid mean energy, and carotid energy PI, provide a more robust framework for understanding the vascularcognitive nexus compared to conventional measures.

Perspectives
In summary, our research demonstrates a robust association between energetic hemodynamic parameters and cognitive function.There exists a strong association between the presence of an increased carotid energy PI, which is characterized by heightened carotid pulsatile energy and decreased carotid mean energy, and impaired cognitive performance, as assessed by the MoCA.Our study provides substantial evidence to support the notion that carotid energy PI and carotid mean energy are more dependable indicators of cognitive decline compared to conventional hemodynamic parameters that rely on flow or pressure measurements.This discovery affirms the enhanced explanatory potential of energetic hemodynamic parameters in the association between vascular health and cognitive function.Future emphasis may not be on arterial pressure or blood flow, but rather on energy, which may become the standard unit of measurement.
The carotid energy PI could be a promising therapeutic target because of its significant correlation with cognitive function.To potentially slow down the progression of vascular dementia, it is recommended to lower carotid energy PI by reducing carotid pulsatile energy, increasing aortic compliance, and decreasing carotid/cerebral resistance.

Fig. 1
Fig.1The presentation of the hydraulic total, mean, pulsatile, and potential energy (the 1st right column), calculated at the central aorta (top panel) and carotid artery (bottom panel), as a function of time.Three steps were required to conclude the energy calculation.The first step was to calculate the total, mean, and pulsatile power as a function of time (the 2nd right column).The total power (black curve) was calculated as the product of concurrent aortic pressure (black curve, the 1st left column) and aortic flow (black curve, the 2nd left column).Similarly, the mean power (red dash-dot curve) and pulsatile power (blue solid curve) were calculated as the product of concurrent mean

Fig. 2
Fig. 2 Differential aortic or carotid hemodynamics in relation to cognitive function.A The correlation between hemodynamics and cognitive function; B The correlations between cognitive function and mean energy and pulsatile energy.Coefficients of correlation were all

Fig. 3
Fig. 3 Analysis of the causal mediation of the associations between Z ao and Aortic pressure wave reflection coefficient and cognitive function.A Z ao was indirectly associated with cognitive function through carotid energy pulsatility index, but not by carotid mean energy.Z ao did not have direct effect on cognitive function (beta = −0.0201,p = 0.3591).B Z ao was indirectly associated with cognitive function through carotid energy pulsatility index, but not by carotid mean energy.Carotid mean flow was not associated with cognitive function.C Aortic pressure wave reflection coefficient (Γ Ao ) was associated with cognitive function

Table 1
Characteristics of the study population

Table 2
Flow and energy related variables at ascending aorta and common carotid arteries

Table 4
The comparative associations of carotid energy pulsatility index, carotid flow pulsatility index, aortic energy pulsatility index with MoCA scores